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URL: https://oeis.org/A349571

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A349571
Dirichlet convolution of A048673 with A055615 (Dirichlet inverse of n).
3
1, 0, 0, 1, -1, 2, -1, 4, 4, 3, -4, 4, -4, 5, 6, 13, -7, 6, -7, 5, 10, 6, -8, 10, 5, 8, 24, 9, -13, -2, -12, 40, 12, 9, 16, 16, -16, 11, 16, 11, -19, -2, -19, 8, 14, 14, -20, 28, 19, 9, 18, 12, -23, 26, 22, 21, 22, 15, -28, 2, -27, 18, 26, 121, 28, -8, -31, 11, 28, -8, -34, 46, -33, 20, 18, 15, 34, -8, -37, 29, 124
OFFSET
1,6
COMMENTS
Also Dirichlet convolution of A349385 with A349387.
FORMULA
a(n) = Sum_{d|n} A048673(n/d) * A055615(d).
a(n) = Sum_{d|n} A349385(n/d) * A349387(d).
MATHEMATICA
f[p_, e_] := NextPrime[p]^e; s[1] = 1; s[n_] := (1 + Times @@ f @@@ FactorInteger[n])/2; a[n_] := DivisorSum[n, # * MoebiusMu[#] * s[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 23 2021 *)
PROG
(PARI)
A048673(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (1/2)*(1+factorback(f)); };
A055615(n) = (n*moebius(n));
A349571(n) = sumdiv(n, d, A048673(n/d)*A055615(d));
CROSSREFS
Cf. A048673, A055615, A349385, A349387, A349572 (Dirichlet inverse).
Cf. also A349398, A349573.
Sequence in context: A101621 A086484 A349572 * A091335 A362865 A274883
KEYWORD
sign
AUTHOR
Antti Karttunen, Nov 23 2021
STATUS
approved